CJC 2024.H2.Phy.PRELIM.P3 - QP

CANDIDATE NAME CLASS 2T PHYSICS 9749/03 Paper 3 Longer Structured Questions 10 September 2024 2 hours Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name and class in the spaces at the top of this page. Write in dark blue or black pen on both sides of the paper. You may use an HB pencil for any diagrams, graphs or rough working. Do not use staples, paper clips, glue or correction fluid. The use of an approved scientific calculator is expected, where appropriate. Answer all questions. Section A Answer all questions. Section B Answer one question only. You are advised to spend one and a half hours on Section A and half an hour on Section B. The number of marks is given in brackets [ ] at the end of each question or part question. This document consists of 27 printed pages and one blank page. [Turn over FOR EXAMINER’S USE SECTION A Q1 / 8 Q2 / 9 Q3 / 8 Q4 / 12 Q5 / 7 Q6 / 8 Q7 / 8 SECTION B Q8 / 20 Q9 / 20 PAPER 3 / 80 PAPER 2 / 80 PAPER 1 / 30 PAPER 4 / 55 TOTAL (WEIGHTED) % Catholic Junior College JC2 Preliminary Examinations Higher 2

2 DATA speed of light in free space c = 3.00 x 108 m s-1 permeability of free space 0 = 4 x 10-7 H m-1 permittivity of free space 0 = 8.85 x 10-12 F m-1 (1/(36)) x 10-9 F m-1 elementary charge e = 1.60 x 10-19 C the Planck constant h = 6.63 x 10-34 J s unified atomic mass constant u = 1.66 x 10-27 kg rest mass of electron me = 9.11 x 10-31 kg rest mass of proton mP = 1.67 x 10-27 kg molar gas constant R = 8.31 J K-1 mol-1 the Avogadro constant NA = 6.02 x 1023 mol-1 the Boltzmann constant k = 1.38 x 10-23 mol-1 gravitational constant G = 6.67 x 10-11 N m2 kg-2 acceleration of free fall g = 9.81 m s-2

3 [Turn over FORMULAE uniformly accelerated motion s = u t + ½ a t2 v2 = u2 + 2as work done on / by a gas W = p V hydrostatic pressure p = gh gravitational potential  = - Gm r temperature T / K = T / ˚C + 273.15 pressure of an ideal gas p = 1 3 Nm V 〈c2〉 mean translational kinetic energy of an ideal gas molecule E = 3 2 kT displacement of particle in s.h.m. x = x0 sin t velocity of particle in s.h.m. v = v0 cos t = 22 0 xx −  electric current I = Anvq resistors in series R = R1 + R2 + ... resistors in parallel 1/R = 1/R1 + 1/R2 + ... electric potential V = Q 4πεor alternating current / voltage x = x0 sin t magnetic flux density due to a long straight wire B = μoI 2πd magnetic flux density due to a flat circular coil B = μoNI 2r magnetic flux density due to a long solenoid B = μonI radioactive decay x = x0 exp(-t) decay constant λ = 1 2 ln2 t

4 Section A Answer all questions in the spaces provided. 1 (a) An object Q of weight 30.0 N is supported by two ropes A and B as shown in Fig. 1.1. Rope A is at an angle  to the vertical and exerts force FA on Q. Rope B is at an angle  to the vertical and exerts a force FB on Q. The angle  of rope B is varied from 0° to 90°. The force FA is varied in magnitude and direction to keep Q in equilibrium. (i) Determine the magnitude of force FA when the angle  is 35° and FB is 20.0 N. magnitude of FA = ……………………………… N [3]   FB FA 30.0 N Fig. 1.1 rope B rope A Q

5 [Turn over (ii) Explain why angles  and θ cannot be 90° at the same time. ………………………………………………….……………………………………………… ………………………………………………….……………………………………………… ………………………………………………….……………………………………………… …………………………………………………….……………………………………. [2] (b) A uniform metal rod AB is freely pivoted at end A as illustrated in Fig. 1.2. The end B is suspended by a light spring. The other end of the spring is supported at Z. The rod is in equilibrium. Fig. 1.2 The spring is now aligned vertically along YB so that the angle between the rod and the spring is no longer 90°. The rod remains in equilibrium in the same position. Explain why the spring force increases. …………………………………………..…………….……………………………………………… …………………………………………..…………….……………………………………………… …………………………………………..…………….……………………………………………… …………………………………………..…………….……………………………………………… …………………………………………..…………….……………………………………………… ………………………….……………………………………………………………………… [3] [Total: 8] B A Z Y

6 2 Two spheres A and B approach each other as illustrated in Fig. 2.1. Fig. 2.1 Sphere A has a mass of 0.500 kg and moves to the right with a speed of 7.40 m s-1. Sphere B has a mass of 0.350 kg and moves to the left with a speed of 9.60 m s-1. The spheres collide and are in contact for a time of 0.400 s. Sphere B reverses its direction of motion and moves off with a speed of 10.4 m s-1. (a) Using momentum consideration, e xplain quantitatively why spheres A and B cannot be at rest at the same instant. …………………………………………..……………….…………………………………………….. …………………………………………..…………….……………………………………………….. …………………………………………..…………….……………………………………………….. .………………………………………………………………………………………………….. [2] (b) For the time during the collision, calculate the average force between the spheres. average force = ……………………………… N [2] 7.40 m s-1 9.60 m s-1 0.350 kg 0.500 kg A B 10.4 m s-1 A B Before collision After collision

7 [Turn over (c) Use your answer in (b) to determine the magnitude of the velocity of sphere A after the collision. Explain your working. magnitude of velocity = ……….………………… m s-1 [3] (d) By considering quantitatively the relative speeds of approach and of separation of the two spheres, deduce whether the collision is elastic or inelastic. ………………………………………………………………………………………………………….. ………………………………………………………………………………………………………….. …………………………………………………………………………………………………… [2] [Total: 9]

8 3 (a) Copper has one conduction electron per atom. The density of copper is 8960 kg m -3. The mass of one mole of copper is 63.5 g. Show that the number density of charge carriers in copper is 8.49 x 1028 m-3. [3]

9 [Turn over (b) A composite wire XYZ is made by connecting in series two uniform wires, each of length L and made of copper but having different diameters as shown in Fig. 3.1. One wire has diameter d and the other wire has diameter 2d. Fig. 3.1 A potential difference is then applied across X and Z of the wire and a current flows through the wire. On Fig. 3.2, sketch a graph to show how the drift velocity vd of electrons through the composite wire varies with distance along the wire from end X to end Z. Fig. 3.2 [3] (c) The mean speed of a conduction electron in the wire is very much greater than the drift velocity of the conduction electrons in the wire. Explain this observation. ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………….. [2] [Total: 8] vd distance from end X 0 L 2L X Y Z d 2d L L

10 4 A mass m is suspended from a vertical spring of spring constant k attached to a fixed support. The mass is pulled down and held at a vertical displacement of 0.16 m from its equilibrium position, as shown in Fig. 4.1. Fig. 4.1 The mass is released. (a) Show that the mass’s acceleration a is